Chapter 1.1, Problem 27E

To determine

To graph: The given function and its parent function and then to describe the transformation.

Answer to Problem 27E

The graph of $f(x)=3x+2$ is a vertical stretch by a factor of $3$ and a vertical translation of $2units$ upward with respect to the graph of the parent linear function.

Explanation of Solution

Given information: Given function is $f(x)=3x+2$ .

Graph:

The function $f$ is a linear function. Using a table of values to graph the given function and the parent function $g(x)=x$ ,

  $\begin{array}{lll}x\hfill & g(x)=x\hfill & f(x)=3x+2\hfill \\ -2\hfill & -2\hfill & -4\hfill \\ -1\hfill & -1\hfill & -1\hfill \\ 0\hfill & 0\hfill & 2\hfill \\ 1\hfill & 1\hfill & 5\hfill \\ 2\hfill & 2\hfill & 8\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $f$ (shown by blue colored line) is a vertical stretch by a factor of $3$ and a vertical translation of $2units$ upward w.r.t. the graph of the parent linear function $g(x)=x$ (shown by green colored line).

So, the graph of $f(x)=3x+2$ is a vertical stretch by a factor of $3$ and a vertical translation of $2units$ upward with respect to the graph of the parent linear function.